$title piped projection and counts to 1,2,3 dimensions and sorts (PIPE6,SEQ=116)

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Contributor: Alex Meeraus
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$version 137 goto OK
$clearError
$stop
$label OK

* the right side has two identical domains
* we match the name without aliasing

$eolCom  //

set i / 1*5 /; alias(i,i1,i2,i3,i4);

parameter a4(i1,i2,i2,i4);   // note the declaration i2,i2

a4(i1,i2,i3,i4)$(uniform(0,1) > .9) = uniform(1,2);

parameters three123L(i1,i2,i3)
           three123R(i1,i2,i3)
           three432L(i4,i3,i2)
           three432R(i4,i3,i2)
           three312L(i3,i1,i2)
           three312R(i3,i1,i2)
           two12L(i1,i2)
           two12R(i1,i2)
           two34(i3,i4)
           two41(i4,i1)
           two23L(i2,i3)
           two23R(i2,i3)
           two24L(i2,i4)
           two24R(i2,i4)
           one1(i1)
           one2L(i2)
           one2R(i2)
           one4(i4);

option one1  < a4
       one2R < a4
       one2L <= a4
       one4  < a4 ;

abort$sum(i1, one1 (i1) <> sum((   i2,i3,i4)$a4(i1,i2,i3,i4), 1)) 'bad aggreagtion';
abort$sum(i2, one2L(i2) <> sum((i1,   i3,i4)$a4(i1,i2,i3,i4), 1)) 'bad aggreagtion';
abort$sum(i2, one2R(i2) <> sum((i1,   i3,i4)$a4(i1,i3,i2,i4), 1)) 'bad aggreagtion';
abort$sum(i4, one4 (i4) <> sum((i1,i2,i3   )$a4(i1,i2,i3,i4), 1)) 'bad aggreagtion';

$exit

option two12R <  a4
       two12R <= a4
       two34  <  a4
       two41  <  a4
       two23R <  a4
       two23L <= a4
       two24L <  a4
       two24R <  a4

abort$sum((i1,i2), two12L(i1,i2) <> sum((      i3,i4)$a4(i1,i2,i3,i4), 1)) 'bad aggreagtion';
abort$sum((i1,i2), two12R(i1,i2) <> sum((      i3,i4)$a4(i1,i3,i2,i4), 1)) 'bad aggreagtion';
abort$sum((i3,i4), two34 (i3,i4) <> sum((i1,i2      )$a4(i1,i2,i3,i4), 1)) 'bad aggreagtion';
abort$sum((i4,i1), two41 (i4,i1) <> sum((   i2,i3   )$a4(i1,i2,i3,i4), 1)) 'bad aggreagtion';
abort$sum((i2,i3), two23L(i2,i3) <> sum((i1      ,i4)$a4(i1,i2,i3,i4), 1)) 'bad aggreagtion';
abort$sum((i2,i3), two23R(i2,i3) <> sum((i1      ,i4)$a4(i1,i3,i2,i4), 1)) 'bad aggreagtion';
abort$sum((i2,i4), two24L(i2,i4) <> sum((i1   ,i3   )$a4(i1,i2,i3,i4), 1)) 'bad aggreagtion';
abort$sum((i2,i4), two24L(i2,i4) <> sum((i1   ,i3   )$a4(i1,i3,i2,i4), 1)) 'bad aggreagtion';

option three123 < a4
       three432 < a4
       three312 < a4;

abort$sum((i1,i2,i3), three123L(i1,i2,i3) <> sum(i4$a4(i1,i2,i3,i4), 1)) 'bad sort';
abort$sum((i1,i2,i3), three123R(i1,i2,i3) <> sum(i4$a4(i1,i3,i2,i4), 1)) 'bad sort';
abort$sum((i4,i3,i2), three432L(i4,i3,i2) <> sum(i1$a4(i1,i2,i3,i4), 1)) 'bad sort';
abort$sum((i4,i3,i2), three432R(i4,i3,i2) <> sum(i1$a4(i1,i3,i2,i4), 1)) 'bad sort';
abort$sum((i3,i1,i2), three312L(i3,i1,i2) <> sum(i4$a4(i1,i2,i3,i4), 1)) 'bad sort';
abort$sum((i3,i1,i2), three312R(i3,i1,i2) <> sum(i4$a4(i1,i3,i2,i4), 1)) 'bad sort';